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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.
波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。
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One over two squared minus one over n squared 3 4 5 where n takes values three, four, five, six.
除以，2，的平方再减去1除以n的平方,将n赋值为。
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And I have this, to write it out, this is order the length of the list squared, OK?
我得写下来,这是把列表的长度平方，对么？
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So, the way to measure force is in kilogram meters per second squared.
所以,力的单位是千克米每秒平方
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They go up at rates squared.
它们以平方的速度增长
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So you see what it is--it's a measure of how much x deviates from the mean, but it's squared.
你会看到,这个指标,衡量的是x与平均值的偏离,而且这里有个平方
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Like what the heck have we been spending our time for-- our time on with Bubble Sort and with Selection Sort and in fact there's plenty of other N squared sorts that we're not even gonna bother looking at.
真见鬼，我们竟然在-,冒泡排序和选择排序上花时间,而事实上，还有很多我们根本都不想考虑的,复杂度为N平方的排序方法。
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b It's RT over molar volume minus b minus a over molar volume V squared.
它等于RT除以摩尔体积V杠减去,再减去a除以摩尔体积的V杠平方。
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And the person we have to thank for actually giving us this more concrete way to think about what a wave function squared is is Max Born here.
需要感谢，马克思，波恩,给了我们，这个波函数平方的,具体解释，事实上。
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We can't actually go ahead and derive this equation of the wave function squared, because no one ever derived it, it's just an interpretation, but it's an interpretation that works essentially perfectly.
从这个方程中,导出，波函数的平方，没有人可以这样做，这仅仅是一种解释，但这种解释，能解释的很好，自从它第一次被提出来之后。
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So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是４πｒ的平方，乘以厚度ｄｒ
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This depiction of matter takes you right up to E=MC E=MC And, that's all he had to work with for data.
物质的叙述，让我们一直等到,的平方，天才。，squared。，Brilliant。,那是他研究数据所得出的成果。
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I want to then do, I need to find the square root b squared plus h squared, right?
我接下来要求b的平方和h的平方,的和的平方根对不对？
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So if we're talking about probability density that's the wave function squared.
如果我们要讨论概率密度,这是波函数的平方。
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Thank you. Sorry, I've got the wrong glasses on but you're absolutely right, and in case the rest of you didn't hear it, n squared.
我看不清，但你绝对是对的,你们其他人可能没听清,是n的平方。
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b If we put it as minus b, that's just equal to a over V squared.
如果我们写成负，这里就等于a除以V的平方。
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Equals a over molar volume squared.
等于a除以摩尔体积的平方。
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Ever since this was first proposed, there has never been any observations that do not coincide with the idea, that did not match the fact that the probability density is equal to the wave function squared.
从未有，任何观测，与它相抵触,从没有过，波函数的平方不等于,概率密度的情况，关于马克思，波恩。
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But luckily we don't have to worry about how we're going to picture all this, now that I said that, no physical interpretation f or a wave function, there is a physical interpretation for what a wave function squared means.
如何想象这些图像,我这么说，虽然波函数，物理解释,但波函数的平方，有物理解释,当我们说到。
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So this squared at the origin is going to be a very high probability, and it decays off as you get farther and farther away from the nucleus or from the center, and that's independent of the angle.
所以这个平方,在原点处非常高，随着离核子的距离,越来越远,它逐渐衰减，并且它和角度是没有关系的。
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A joule is a kilogram meter squared per second squared.
一个焦耳等于,一千克乘以米的平方除以秒的平方。
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So instead of being equal to negative z squared, now we're equal to negative z effective squared times r h all over n squared.
这里不再等于-z的平方，现在我们等于-有效的z的平方,乘以RH除以n的平方。
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Acceleration is measured in meters per second squared.
加速度的单位是米每秒平方
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I can either look at my flow chart, or I can look at the code. If I look at the flow chart, it says, I'm at this point. Look at ANS squared. Is it less than or equal to-- sorry, first of all, 0 ANS squared is 0, is it less than or equal to x, yes.
我可以看流程图也可以看我的代码,如果我看流程图的话，流程图这么说的，在这一点，看看ANS的平方,看是不是小于等于-对不起，首先，ANS的平方是。
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OK. If b is even, then a to the b is the same as a squared all to the b over 2.
就等于a的平方的二分之b次方,好，就是把二挪到外面来了。
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You see an object in motion, you find a and you give a a certain numerical value, 10 meters per second squared.
你看到一个物体在运动,你会发现它的 a,然后给 a 赋值,10 米每秒平方
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And that's going to be equal to negative z effective squared times r h over n squared.
有效的z的平方,乘以RH除以n的平方。
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N --O So we introduced this notation big O which generally refers to worst case.
的平方。，So，，N，squared。,这里我们介绍一个符号,它泛指最坏的情况。
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I'm going to start with a guess, I'm going to call it g. And then I'm going to say, if g squared is close to x, stop.
我会从一个猜想开始，把它叫做g，然后我会说，如果g的平方接近于X，打住。
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